A Lommel polynomial Rm,ν(z) is a polynomial in 1/z giving the recurrence relation J m + ν ( z ) = J ν ( z ) R m , ν ( z ) − J ν − 1 ( z ) R m − 1 , ν + 1 ( z ) {\displaystyle \displaystyle J_{m+\nu }(z)=J_{\nu }(z)R_{m,\nu }(z)-J_{\nu -1}(z)R_{m-1,\nu +1}(z)} where Jν(z) is a Bessel function of the first kind. They are given explicitly by R m , ν ( z ) = ∑ n = 0 [ m / 2 ] ( − 1 ) n ( m − n ) !
A Lommel polynomial Rm,ν(z) is a polynomial in 1/z giving the recurrence relation J m + ν ( z ) = J ν ( z ) R m , ν ( z ) − J ν − 1 ( z ) R m − 1 , ν + 1 ( z ) {\displaystyle \displaystyle J_{m+\nu }(z)=J_{\nu }(z)R_{m,\nu }(z)-J_{\nu -1}(z)R_{m-1,\nu +1}(z)} where Jν(z) is a Bessel function of the first kind. They are given explicitly by R m , ν ( z ) = ∑ n = 0 [ m / 2 ] ( − 1 ) n ( m − n ) !
Source: Wikipedia "Lommel polynomial" · CC BY-SA 4.0
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